I see a lot of threads about the same problem, so I tried to make a photo that helps.
If you've got fuel "overflowing" into the carb, chances are this is the problem. Make sure you've got an ignition sourced 12v to the clip. Hopefully this will solve a lot of the guessing. If someone's got a better pic, please post it.

 

bump back to the top for a bit.

 

What you have cirlcled in the picture is the thermo swich for the choke. If you have a fuel leak to the secondaries check the floats. To do this you have to remove the air horn which is done by all the phillips head screws on the top of the carb. Search the forum for a STERLING write up about carb rebuilding and tuning. Contains lots of useful inforamation.

 

No disrespect intended, but I don't think it's good advice to open up the carb unless absolutely nessacary (sp?). There always seems to be a greater issue afterwards. This is a simple process, and may be the most productive 5 minutes you ever spend on your carb.

Here's the process:
I would only rebuild the carb as a last resort. You may do more harm than good. If the solenoid is the problem, it may not need replaced. There's a good chance that the 20+ year old wire is faulty.

Test for 12 volts with the ignition on. If voltage is present, leave the key on, un plug the solenoid, and plug it back in. You should be able to hear it actuate, it'll be a pretty distinct and audable "CLICK". If it doesn't click it's a bad solenoid, and There's probably a lot of them around the forum for little or nothing.

If you don't have the 12 volts when you test it, run a test wire from the battery, touch it to the solenoid connector, and listen for the click. if it clicks, run a new wire from an ignition source, re-use the old connector, or a crimp (your choice), and it should be fixed.

DON"T FORGET TO UN-FLOOD THE MOTOR BEFORE STARTING IT UP. A flooded motor can be a bear to start.
Good luck.

 

how do you unflood a motor